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Co-optimization of Enhanced Oil Recovery and Carbon
Sequestration
Abstract
This paper presents an economic analysis of CO2-enhanced oil recovery (EOR). EOR entails
injection of CO2 into mature oil fields, thereby increasing the rate of extraction. As part
of this process, significant quantities of CO2 can remain sequestered in the reservoir. We
develop a theoretical framework that analyzes the dynamic co-optimization of oil extraction
and CO2 sequestration, through CO2 injection. Numerical simulations, based on an ongoing
EOR project in Wyoming, show that cumulative sequestration is positively related to the oil
price, and is in fact much more responsive to oil-price increases than to carbon tax increases.
Keywords: climate change, carbon sequestration, enhanced oil recovery
JEL classification: Q32; Q40
2
1. Introduction
There is a growing consensus in both policy circles and in the energy industry that within
the next few years, the US Federal government will adopt some form of regulation of CO2
emissions.1,2 At the same time, it is widely believed that much of the nation’s energy supply
over the coming decades will continue to come from fossil fuels, coal in particular (MIT;
2007). Many analysts believe the only way to reconcile the anticipated growth in the use of
coal with anticipated limits on CO2 emissions is through the development and deployment
of carbon capture and geological sequestration (CCS). There seems to be broad agreement
that the first geologic sequestration projects are likely to be those exploiting CO2-enhanced
oil recovery (EOR).3
This technique, which has been used successfully in a number of oil plays (notably
in West Texas, Wyoming, and Saskatchewan), entails injection of CO2 into mature oil fields
in a manner that causes the CO2 to mix with some fraction of the oil that still remains
underground. Doing so reduces the oil’s viscosity, thereby making it possible to extract
additional, otherwise unrecoverable oil.4 Although some of the CO2 resurfaces with the oil,
it can be separated from the output stream, recompressed, and reinjected. Eventually, when
the EOR project is terminated, all the injected CO2 is sequestered.
EOR is a “game-changing” technology for the recovery of oil from depleted reserves.
Estimates suggest that recovery rates for existing reserves could be approximately doubled,
1 Consider that among the recent candidates for the US presidency, John McCain was the lead author ofa Senate proposal to reduce carbon emissions by 65 percent by 2050, while Barack Obama is on record assupporting a cut in carbon emissions of 80 percent by 2050. (Scott Horsley, 2005 Election Issues: ClimateChange, National Public Radio, http://www.npr.org/news/specials/election2005/issues/climate.html).2 For example, the Vice President of Environmental Policy for Duke Energy stated in a Washington Postarticle, “Our viewpoint is that it’s going to happen. There’s scientific evidence of climate change. We’d liketo know what legislation will be put together so that, when we figure out how to increase our load, we knowexactly what to expect.” (Steven Mufson and Juliet Eilperin, “Energy Firms Come to Terms With ClimateChange,” Washington Post, Saturday, November 25, 2005, p. A01)3 This view was expressed succinctly in recent testimony by George Peridas, Science Fellow at the NationalResources Defense Council, who said that CO2-EOR “has a substantial immediate- to long- term role toplay in both increasing domestic oil production in a responsible way, and in sequestering CO2” (?). Seealso the recent Congressional testimony by William Townsend (Townsend; 2007) and the recent report HardTruths: Facing the Hard Truths About Energy, (NPC; 2007).4 Other methods of enhanced oil recovery exist as well, including injection of nitrogen, methane, and variouspolymers. Because these methods are not the focus of this paper, we use the term enhanced oil recovery, orEOR, as shorthand for CO2-enhanced oil recovery.
3
while the application of EOR on a broad scale could raise domestic recoverable oil reserves
in the United States by over 80 billion barrels (?). Similarly, Shaw and Bachu (2003) claim
that 4,470 fields, just over half of the known oil reservoirs in Alberta, are amenable to
CO2 injection for enhanced oil recovery. Babadagli (2006) states that enhanced oil recovery
applied in these reservoirs could translate in an additional 165 billion barrels of oil recovered
and over 1 Gt of CO2 sequestration. (Snyder et al.; 2008) estimate that at current oil and
carbon prices and with current technology, approximately half of this capacity is economically
viable.
In this paper, we present what is to our knowledge the first theoretical economic
analysis of CO2-enhanced oil recovery. In the tradition of Hotelling (1931), an oil field
contains a physical quantity of oil which the producer seeks to extract at a particular rate
over time so as to maximize the economic rents from extraction. The ability to enhance
oil extraction rates through injection of CO2 alters this extraction problem in a number of
non-trivial ways.
First, CO2 is not a costless input. Significant up-front investments are required
to make production and injection wells suitable for CO2 use. In addition, maintaining a
given injection rate over time requires continuous purchases make up for the fraction of
injected CO2 that remains sequestered in the reservoir. Separating the remaining fraction
that resurfaces with the produced oil, and then dehydrating and recompressing it, is costly
as well, requiring both up-front capital costs and variable processing costs.
Second, even at a constant injection rate, the amount of oil recovered declines over
time, as does the fraction of injected CO2 that remains sequestered in the reservoir. Both
the producer’s revenue stream and cost stream are therefore time varying.
Third, while sequestration of CO2 currently yields no economic benefits in juris-
dictions without carbon emissions restrictions, future regulations of CO2 emissions in the
context of climate-change policies may generate such benefits if EOR projects are allowed to
earn credits for units of CO2 sequestered. The producer’s objective would then be the maxi-
mization of the combined revenue streams from both oil production and CO2 sequestration,
net of CO2 purchase and recycling costs.
4
Fourth, carbon taxes affect these revenue and cost streams in multiple ways. While a
carbon tax effectively reduces the input cost for EOR and increases the net present value of
the CO2storage potential of the oil field, the incidence of the tax on the price of oil reduces
the value of the traditional use of the asset.
Fifth, in addition to these economic tradeoffs, fluid-dynamic interactions of CO2,
water, and oil inside the reservoir give rise to a further, physical tradeoff faced by the pro-
ducer. Whereas injecting pure CO2 maximizes oil recovery from the area of the reservoir
that the CO2 sweeps through, that area itself may be small, as pure CO2 tends to “finger”
or “channel” between injection and production wells, bypassing some of the oil. In compar-
ison, injecting pure water increases the area that is swept, but reduces recovery from that
area. Reservoir-engineering studies5 indicate that both oil recovery and CO2 sequestration
are maximized when a mix of CO2 and water is injected (whereby the CO2 fraction that
maximizes oil recovery typically differs from that maximizing sequestration).
Our paper provides an evaluation of the role of all five factors. We start by developing
a theoretical framework that analyzes the dynamic co-optimization of oil extraction and CO2
sequestration, through the producer’s choice at each point in time of an optimal CO2 fraction
in the injection stream (the control variable). The decision to cease extraction is determined
by a transversality condition. Both the injection and termination decisions depend in part
on the anticipated price of oil and the carbon tax or credit price. The paper concludes
with a series of simulations that are based on an ongoing project, namely the Lost Soldier-
Tensleep field in Wyoming. These simulations generate time paths of CO2 injections. In
turn, these time paths of injection imply time paths of oil extraction; comparing against
the corresponding time path of oil production under secondary production (which relies on
injecting water but not gas) allows one to estimate the additional volume of oil produced
under EOR and the amount of CO2 that is ultimately sequestered. It also allows estimation
of the net present value of incremental profits from EOR (over and above those that would
5 See, e.g., Al-Shuraiqi et al. (2003), Jessen et al. (2005), Juanes and Blunt (2006), Guo et al. (2006), andTrivedi and Babadagli (2007).
5
be earned by continuing secondary production), and thereby of the potential contribution
that EOR might make to the development of CCS infrastructure.
2. The Model
Our model of oil production is based on the physical reality that input injections (water,
gas, or some mixture of the two) must balance with fluid output (oil, water, and gas).6 In
addition, the rate of oil production is linked to remaining reserves by the so-called “decline
curve.”7 This relation specifies output as a particular fraction of remaining reserves, where
that fraction is itself linked to the fraction of CO2 in the injection stream. Upon specifying
the relation between rate of CO2 injection and oil production we may write down the formal
dynamic optimization model, which we then use to describe the time path of CO2 injection.
Ultimately, this allows us to describe the rate of CO2 that is sequestered at every point in
time, and thereby to determine the total amount sequestered.
We begin with some notation. Let the physical capacity of input injections be I,
which can be thought of as the capacity of the injecting wells. We write the rate of CO2
injection at time t as c(t), and the rate of water injection at time t as hi(t). We assume the
total rate of injection is constant across time. This reflects the fact that CO2-EOR projects
are usually operated at “minimum miscibility pressure,” which is the minimum pressure
required to make the CO2 mix with the oil. Maintaining that pressure requires a roughly
constant overall injection rate. In light of this assumption, c(t) + hi(t) = I at each point in
time.
Let the rate of oil production at time t be q(t), the rate of CO2 production (or
“leakage”) at time t be `(t), and the rate of water production at time t be hp(t). Materials
6 Reservoir engineers refer to this as “materials balance.” It should be noted that this requirement appliesat the temperature and pressure conditions that obtain inside the reservoir. At these conditions, CO2 existsin a highly compressed, “supercritical” state and behaves much like a fluid.7 Fetkovitch (1980) provides an in-depth discussion of decline curves, and of the justification for their wide-spread use in predicting oil production from reservoirs.
6
balance then requires that
q(t) + l(t) + hp(t) = c(t) + hi(t)
at each point in time (with both sums equaling I). The leaked CO2 can be vented or recycled.
Let the price of a unit of newly purchased CO2 equal ws and the unit cost of recycling CO2
equal w`. We assume that ws > w`, so that it is cheaper for the firm to recycle than to vent.8
Since all leakage is re-injected, total CO2 injection is the sum of new purchases and
leakage, or
c(t) = s(t) + `(t). (1)
The rate at which CO2 is sequestered depends on the linkage between injected CO2 and
produced oil. We assume that the fraction of oil production displaced by CO2 (as opposed
to that displaced by water) is proportional to the fraction of CO2 in the total injection
stream. We also assume that sequestered CO2 takes up the underground space vacated by
the oil that it displaces. To simplify the exposition, units of oil are chosen such that in the
reservoir, vacating the space taken up by one unit of oil creates space for sequestering exactly
one unit of CO2. As a result, we have s(t) = c(t)q(t)/I. As we are focusing on an individual
firm and a particular oil reservoir, we may normalize so that I = 1. Accordingly,
s(t) = c(t)q(t). (2)
At any point in time, the amount of recoverable oil is R(t); we write the initial amount
of oil at the moment the EOR project is undertaken as R0. As usual, this variable plays the
role of the state variable in our analysis, and it evolves via
R = −q. (3)
8 In practice, the purchase price of CO2 is several times higher than the cost of recycling. Thus, firmsundertaking EOR do generally recycle CO2. Importantly, the presence of a carbon price τ does not changethe relevant comparison: the cost of a newly purchased unit becomes ws− τ (as the seller of the CO2 avoidsthe carbon tax or receives a credit for sequestering), while the opportunity cost of recycling becomes w` − τ(as venting would obligate the producer to pay the carbon tax or purchase a credit).
7
In keeping with the physical reality of oil recovery, we assume that the rate of production can
be described by a decline curve: q(t) = δR(t). In our setting, however, the ratio of output to
reserves—which plays the role of the decline rate—is linked to the rate of injection: δ = δ(c).
We therefore have the relation
q(t) = δ(c)R(t). (4)
Combining (3) and (4), we obtain
R = −δ(c)R. (5)
Consistent with results from the reservoir-engineering studies cited in the introduction, we
assume that the δ(c) function relating the rate of injection to the decline rate is concave,
with an interior maximum. If only water is used (termed a “waterflood”), the decline rate
is δw ≡ δ(0) > 0. If only CO2 is used (termed a “pure CO2 flood”), the decline rate is δ(1).
We assume, consistent again with reservoir-engineering studies, that δ(1) > δw. In light of
the concavity of δ(c), δ′(0) > 0 > δ′(1).
The economic environment depends on three ingredients: the price of oil, p; the carbon
tax, τ ; and operating costs. We assume that all costs other than those of CO2 purchases
and CO2 recycling are tied to the overall amount of fluids injected and the amount of fluids
produced. As both amounts are constant and equal to I, these other costs are a constant F .
Accordingly, the firm earns a rate of profits equal to
π = pq − (ws − τ)s− w``− F.
Using (1), (2), and (5), we may rewrite the profit rate as
π = pδ(c)R− [ws − τ ]cδ(c)R− w`c[1− δ(c)R]− F
= pδ(c)R− [ws − τ − w`]cδ(c)R− w`c− F. (6)
Since the combustion of oil generates CO2 as a by-product, it seems reasonable to expect
that there will be a tax liability embedded within the market price. To facilitate further
discussions of the role played by the carbon tax, it will be convenient to isolate this effect in
the expression of profits. To that end, we denote the induced tax liability for a one dollar
8
increase in the carbon tax by β. This parameter combines tax incidence effects with unit
conversions associated with the transformation of a unit of produced oil into carbon units.
Adjusting (6) to take account of these aspects, we may write the rate of profits as
π = (p− βτ)δ(c)R− [ws − τ − w`]cδ(c)R− w`c− F.
To save on notation, we will typically summarize the combination p − βτ as Y and the
combination ws − τ − w` as Z. Using this notational convention, the profit rate is
π = Y δ(c)R− Zcδ(c)R− w`c− F.
3. Analysis
The goal of the firm is to choose a time path of the injection rate c(t) so as to maximize
its present discounted value, subject to the state equation (5), the initial value of the state
variable, R0, and the constraints 0 ≤ c ≤ 1, R ≥ 0. Both the terminal time T and the
terminal stock R(T ) are free, and so the optimal choices of these values will be governed by
transversality conditions. To solve this dynamic optimization problem, we first define the
current-value Hamiltonian
H = π −mq = Y δ(c)R− Zcδ(c)R− w`c− F −mδ(c)R, (7)
where m is the current-value multiplier (shadow price) associated with a unit of oil in situ.
The optimal path of extraction satisfies the maximum principle, which consists of
the state equation, an equation for identifying the optimal extraction rate at a given point
in time, and an equation of motion for the shadow price. If the optimal extraction rate is
described by an interior solution, we have
Hc = (Y − Zc−m)δ′(c)R− Zδ(c)R− w` = 0, (8)
where Hc = ∂H/∂c. Irrespective of whether the optimal value of c is described by an interior
solution, the state equation is given by (5), and the equation of motion for the shadow price
9
is
m = rm− (Y − Zc−m)δ(c). (9)
The right-hand side of eq. (9) duffers from the standard Hotelling representation by virtue
of the second set of terms. These terms capture the fact that current carbon injections
reduce the productive capability of future injections. The value associated with this induced
diminution of the future production rate is the product of the marginal impact of the pro-
duction rate on the current-value Hamiltonian (Y − Zc − m) and the current decline rate
(δ(c)).
Because the end time is free, the value of the current-value Hamiltonian at the ter-
minal time T must be zero. As the end state is free, the product of the shadow price and
the state variable at the terminal time must also be zero: m(T )R(T ) = 0. As the extraction
rate is proportional to the stock, we infer from (7) that the profit rate must be zero at time
T . But for that to happen there must be positive revenues, which in turn requires a positive
production rate. It follows that the terminal stock is positive, so that the terminal value of
the shadow price must be zero.
We now turn to a discussion of the time path of injection. Assuming an interior
solution over an interval, we may time-differentiate (8) to get
c = [−Hcmm−HcRR]/Hcc,
where Hcx = ∂2H/∂c∂x, x = m, c or R. From (8), we see that Hcm = −δ′(c)R and
HcR = (Y − Zc −m)δ′(c) − Zδ(c) = w`/R (where we use (8) to extract the last relation).
Combining these observations with the state equation, we get
c = [δ′(c)Rm+ w`δ(c)]/Hcc. (10)
At an interior solution, the denominator is negative and the second term within square
brackets is positive. It follows that injection is falling at any moment where δ′(c)m is
positive; if it is negative, the sign of c is ambiguous.
10
To further explore the time path of c, we combine (8) and (9) to get
δ′(c)Rm+ w`δ(c) = [rδ′(c)m− Zδ(c)2]R. (11)
Comparing (10) and (11), it is apparent that a sufficient condition for c To be negative
is for the right-hand side of (11) to be positive. This will occur, for example, if δ′ > 0
and Z is not large and positive, or if Z is negative and large in magnitude. Heuristically,
δ′ > 0 is consistent with the notion of restraining current production so as to allow rents
to rise over time, which seems plausible. For Z to be small is a bit less obvious. Recall
that Z = ws − τ − w`, and that by assumption ws − w` > 0. If ws − w` is small, which
is the case in our simulations and seems to be the empirically important case, then Z will
be small irrespective of the size of the carbon tax. On the other hand, if the carbon tax is
particularly large then Z will be negative. On balance, then, the right-hand side of (11) will
be positive in a range of cases that seem empirically relevant. As such, the rate of injection
will commonly be declining.
The preceding discussion focuses on interior solutions. While these will be common,
there are circumstances under which corner solutions obtain. We now discuss those condi-
tions. First, suppose the optimal rate of CO2 injection is zero (i.e., it is optimal to undertake
a waterflood); in that case Hc ≤ 0 when evaluated at c = 0. The condition of interest is
(Y −m)δ′(0)R− ZδwR− ws ≤ 0.
Because m and R do not change discontinuously, if this condition holds with strict inequality
at a particular moment t, it must hold for an interval of time following t. Accordingly, during
this interval the optimal level of c remains equal to zero. It follows that during this interval
Hc = −δ′(0)[Rm− (Y −m)R]− ZδwR,
or, upon using (5),
Hc = −{δ′(0)[m+ δw(Y −m)]− Zδ2
w
}R. (12)
11
Combining (9) and (12), taking note of the fact that c = 0, we deduce that
Hc = −[rmδ′(0)− Zδ2w]R. (13)
The important thing to note here is that for negative values of Z, or values of Z that are
positive but relatively small in magnitude, the right-hand side of (13) will be non-positive; as
we noted above, this restriction does not seem to be terribly demanding. In such a scenario,
once Hc becomes negative, it tends to stay negative. We conclude that it will be typical for
the corner solution c = 0 to remain in effect once it is initiated.
Now suppose the optimal rate of CO2 injection is one (i.e., it is optimal to undertake
a pure CO2 flood); in that case Hc ≥ 0 when evaluated at c = 1. The condition of interest is
(Y − Z −m)δ′(1)R− Zδ(1)R− ws ≥ 0.
As with the c = 0 corner solution, if this condition holds with strict inequality, it must apply
for an interval of time; during that interval we have
Hc = −[rmδ′(1)− Zδ(1)2]R. (14)
As noted above, the only way this corner solution can obtain is if Z is negative and large
in magnitude. On the other hand, δ′(1) < 0. Thus, depending on the relative magnitudes
of Z and m, Hc can either be rising or falling. Importantly, as m is likely to fall over
time, eventually Hc will become negative. It follows that the pure CO2 flood cannot last
indefinitely: at some point, it will be optimal to adopt an interior solution.
4. Simulation Framework
In order to add greater context to the results derived above, we have solved and simulated
the model numerically to yield optimal time paths of carbon injection rates for various
combinations of oil price and carbon tax. Below we first discuss the solution algorithm and
then present results.
12
The optimization problem is reasonably straightforward, in that it involves a single
control variable, CO2 injection c, which is optimized given a single state variable, remaining
physical reserves R. We used two approaches to solving the problem (which yielded virtually
identical results). The first approach was a brute-force determination of the optimal time
path of c. In this approach, a discretized version of the control problem was programmed.
Time was divided into discrete units, so that the function c(t) could be approximated by a
multi-variate function T+1 values c(t), t = 1..., T . The combination of values that maximized
the present value of profits was then identified using standard numerical techniques.
In the second approach the problem was solved by first converting it to discrete time
and then using an algorithm that iterates on an approximation to the solution to the Bellman
equation. Here, the solution to the dynamic program is computed using a neural-network
approximation defined over a finite set of grid points distributed within the state space.9
Let V (R) denote the optimal value function:
V (R) = maxcY δ(c)R− Zcδ(c)R− w`c− F + V (R− δ(c)R). (15)
Write Φ(R|φ) as an approximation of V (R) over a grid defined by neural network parameter
values φ. The algorithm consists of 5 steps:
(1) Draw a distribution of grid points in R space.
(2) Begin with an initial guess of Φ0(R) = 0,∀R and solve (15) given this guess at each
grid point. Denote the solution to this iteration by V 1(R).
(3) Compute the approximation for iteration i = 1, 2, . . . by solving minφ{Φ(R|φ) −
V i(R)}2 and denote the solution Φi(R).
(4) Solve V i+1 = maxc Y δ(c)R− Zcδ(c)R− w`c− F + Φi(R− δ(c)R).
(5) Return to step 3 unless ||V i(R)− V i−1(R)|| < 10−6.
The final approximation, Φ(R, φ), represents an approximate solution to the dynamic pro-
gram.
We compute the solution for scenarios with oil prices of $100, $200, and $300 per
barrel (bl), taking $100/bl as our baseline price, and for carbon taxes of $0, $40, $80, and
9 For a detailed discussion of neural networks see Hassoun (1995).
13
I 1 overall rate of injection and production (×1 million barrels)R0 1 initial stock of oil in reservoir (×1 million barrels)ws 4 per-barrel cost of purchased CO2
w` 1 per-barrel cost of separating and recycling “leaked” CO2
F 0.1 fixed costs (×$1 million)β 1 incidence of the carbon tax on the oil producerr 0.05 discount rateδw 0.06 intercept of δ(c) functionδ1 0.20 first coefficient of δ(c) functionδ2 0.16 second coefficient of δ(c) function
Table 1. Baseline parameter values.
$120 per tonne of CO2 (tCO2), taking the absence of any tax as our baseline. Table 1 shows
the baseline parameter values of the numerical model. All quantity flows are in units of
1 million “reservoir” barrels (rb) per year (1 barrel= 42 gallons (US) ≈ 0.16m3), meaning
barrels at the temperature and pressure conditions that obtain inside the reservoir. Overall
injection I is normalized to 1 million such barrels.
The initial stock of oil in the reservoir, R0 is set at 1 million barrels as well. For
comparison, the Lost Soldier–Tensleep (LSTP) EOR project in Wyoming injects about 44
million barrels per year, and extrapolating the decline curve for its oil production since
starting the CO2 flood suggests that ultimately about 36 million barrels of oil would be
recovered over the course of that flood were it to be continued forever. In effect, then, our
simulation applies a scaling factor of about 1/40 to the LSTP project.
The various cost parameters of the model are based on a variety of sources, including
data presented in McCoy (2008) and EIA (2007), as well as personal communication with
industry experts.10 Oil producers commonly measure CO2 in units of 1,000 cubic feet (mcf)
at standard surface temperature and pressure conditions. In Wyoming, the purchase price
of CO2 is currently about $2 per mcf. To convert this price to reservoir barrels, we have
to take account of the fact that the CO2 is greatly compressed when it is injected into the
reservoir. At LSTP, the compression factor (referred to by reservoir engineers as “formation
volume factor for CO2”) is 0.471 rb/mcf (which, since 1 mcf corresponds to about 178 barrels,
amounts to a compression rate of about 380 times). Rounding this factor up to 0.5, we end
10 In particular, Charles Fox of Kinder Morgan, Inc. and Mark Nicholas of Nicholas Consulting Group.
14
up with a gross CO2 purchase price ws of $4/rb. We take the unit cost w` of separating
and recycling “leaked” CO2 that is mixed in with the produced oil to be on the order of
$0.50/mcf, or $1/rb.
It is important to note at this point that, although we express carbon taxes throughout
the paper in terms of dollars per tCO2, the parameter τ in the numerical model is expressed
in dollars per rb, for conformity with the other prices in the model (including ws and w`).
Since one tCO2 corresponds to about 19.05 mcf, the above-mentioned conversion factor for
LSTP of 0.5 mcf/rb results in a combined conversion factor of 9.5 rb/tCO2, which we round
up to 10. In other words, a carbon tax of $40/tCO2 translates to a per-barrel tax of $4.
Operating costs unrelated to injection or recycling of CO2 amount to about $24,000
per well per year in non-injection or production-related expenses, plus about $0.0125 per
barrel of overall injection or production. Applying our scaling factor of 1/40 to LSTP’s total
of about 110 active wells, each producing or injecting about 800,000 rb per year, this works
out to fixed costs F of about $0.1 million dollars per year.
The parameter β, which we refer to as the carbon tax incidence on oil Producers
below, is actually a combination of tax incidence effects with unit conversions associated
with the transformation of a unit of produced oil into carbon units. Tax incidence effects
depend on supply and demand elasticities. We assume that the elasticity of demand in
global oil markets is around three times as high as the elasticity of supply, implying that the
incidence on producers of a given tax expressed in dollars per barrel of oil is 25%. Based
on data reported in EPA (2007), we estimate the quantity of CO2 generated by combusting
one barrel of oil at around 0.4tCO2, or 4rb. Multiplying this by the incidence of 25%, and
recalling that τ in the numerical model is expressed in dollars per rb, we end up with a
combined incidence parameter of β = 1.11
Lastly, the parameters of δ(c) function are based on a combination of production
experience at LSTP and simulation results in the literature. Specifically, the decline rate of
overall oil production at LSTP since it started its CO2-flood is about 11.5%, whereby the
11 At the end of the next section, we perform some sensitivity analysis on this parameter. Specifically, weconsider the two extreme cases where the incidence is zero, so that β = 0 also, and where the incidence is100%, so that β = 4.
15
fraction of CO2 in overall injection has been held roughly constant over time at about 0.35.
Also, simulation data in Guo et al. (2006) based on data from an oil field in China indicate
that, compared to cumulative oil recovery after 6 years of injecting pure water, recovery after
6 years of injecting a mix of half-CO2 half water is about twice higher, while recovery after
6 years of injecting pure CO2 is about five-thirds higher. These data are roughly consistent
with a quadratic δ(c) function
δ(c) = δw + δ1c− δ2c2
with parameters δw = 0.06, δ1 = 0.2, and δ2 = 0.16. Based on this parameterization, one
finds that δ(0) = 0.06, δ(0.5) = 0.12, and δ(1) = 0.09.
5. Simulation Results
The first element of behavior that we wish to define is the optimal extraction and seques-
tration path for our benchmark assumptions. Here, we use an oil price of $100 (constant
over time) with no carbon tax. Figure 1 shows the optimal paths of CO2 injection (c), CO2
leakage (`), oil production (q), and flow CO2 sequestration (s).
0 10 20 30 40 50
0
0.1
0.2
0.3
0.4
0.5
0.6
Time (years)
Flo
ws
(mill
ion
bl/y
ear)
CO2 injectionCO2 leakageoil productionCO2 sequestration
Figure 1. CO2 injection, leakage, and sequestration, and oil production over time.
The optimal initial injection rate is 0.485 million barrels/year, somewhat smaller
than the instantaneous oil-production maximizing rate of 0.625. This reflects the producer’s
16
tradeoffs of current against future extraction (the myopic profit-maximizing injection rate is
0.582) and of oil revenues against CO2 injection costs. Note also that a large fraction (initially
about 88%) of the injected CO2 resurfaces with the produced oil and must be recycled.
As oil production declines over time from its initial rate of 0.119 million barrels/year, the
producer’s revenues decline as well, as does CO2 sequestration in the space vacated by the
oil. As a result, CO2 leakage, and thereby recycling costs, would increase over time even
if the producer chose to hold CO2 injection constant. This changing balance between oil
revenues and recycling costs makes it optimal for the producer to instead gradually reduce
the injection rate over time, as predicted by the theory.
After about 22 years, the optimal CO2 injection rate drops to zero, at which point
the producer switches to a pure waterflood, thereby completely avoiding CO2 injection costs.
From that point in time forward, profits consist of the (declining) oil revenues less fixed costs.
These remain positive for another 31 years, after which the field is shut down.
5.1. Effects of oil price
Our investigation of the comparative dynamics of the model starts with the effect of higher
oil prices. Panel (a) of Figure 2 shows how the optimal CO2 injection path changes as the
oil price level is raised from a constant $100 to a constant $300/bl. Panel (c) of Figure 2
shows how the optimal time path of oil production changes with price; for reference, we also
plot the time path under pure water flood. The higher resulting oil revenues make it optimal
to initially raise the CO2 injection rate, bringing it closer to the output-maximizing level.
However, because even at the baseline price of $100, initial revenues are already very high
relative to CO2-related costs, baseline oil production is already very close to its revenue-
maximizing rate at each point in time. Raising the price therefore has a negligibly small
effect on the oil production path, as is evident from panel (c) of the graph; it also has
a negligible effect on cumulative oil production, as shown in panel (d). Nevertheless, the
fact that the oil is produced with a more CO2-rich injection mix implies that cumulative
sequestration over the productive lifetime of the field increases, as shown in panel (b) of
Figure 2.
17
0 5 10 15 20 25 30 35 40 45
0
0.1
0.2
0.3
0.4
0.5
0.6
Time (years)
Rat
e (m
illio
n bl
/yea
r)
p $100/blp $200/blp $300/bl
(a)
0 5 10 15 20 25 30 35 40 45
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
Time (years)
Qua
ntity
(m
illio
n bl
)
p $100/blp $200/blp $300/bl
(b)
0 5 10 15 20 25 30 35 40 45
0
0.02
0.04
0.06
0.08
0.1
0.12
Time (years)
Rat
e (m
illio
n bl
/yea
r)
waterfloodp $100/blp $200/blp $300/bl
(c)
0 5 10 15 20 25 30 35 40 45
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Time (years)
Qua
ntity
(m
illio
n bl
)
waterfloodp $100/blp $200/blp $300/bl
(d)
Figure 2. Change in (a) CO2 injection, (b) cumulative sequestration, (c) oilproduction, and (d) cumulative oil production paths as a result of oil pricechanges.
Figure 3 shows oil supply and resulting CO2 sequestration as a function of the oil
price. Panel (a) shows cumulative levels of both, whereas panel (b) shows the annualized
equivalent.12 Note that the CO2 sequestration supply curves are discontinuous at a price of
$52 barrel, below which incremental profits from CO2 injection no longer justify the up-front
12 The annualized values are calculated as the constant rate s or q that, when multiplied by the relevantprice τ or p, would over an infinite time horizon yield the same present value as the actual, time-varying
18
0 0.2 0.4 0.6 0.8 1 1.2 1.4
1.712
50
100
150
200
250
300
Cumulative (million bl)
Oil
pric
e ($
/bl)
CO2 seq.oil prd.
(a)
0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05
1.712
50
100
150
200
250
300
Annualized (million bl/year)
Oil
pric
e ($
/bl)
CO2 seq.oil prd.
(b)
Figure 3. CO2 sequestration and oil production, both cumulative (a) andannualized (b), as a function of the oil price.
investment cost. At lower prices, the producer therefore optimally sticks with a waterflood,
resulting in zero sequestration and in slower oil extraction (hence the downward jump in
annualized production).
Even at $52/bl, the variable costs of CO2 injection are so low, however, that the
optimal oil extraction path is very close to the optimal path that would obtain if variable
costs were zero (i.e., the revenue-maximizing path). As a result, variation in oil prices has
almost no effect on oil output. The effect on sequestration is more substantial, however: at
the baseline price of $100, the elasticity of cumulative sequestration is 0.57, while that of
annualized sequestration is 0.47.
5.2. Effects of carbon tax
We continue our investigation of the comparative dynamics of the model with the effect of
higher carbon taxes. Figure 4 illustrates the effects of higher constant carbon taxes. At
higher constant carbon-tax levels, both the net-of-tax oil price received by the producer and
rate s(t) or q(t). That is, s is implicitly defined by∫ ∞0
e−rtτs dt =∫ ∞
0
e−rtτs(t) dt.
and q is defined analogously.
19
the net-of-tax input price of CO2 are lower. However, at a given injection rate c(t), the
change in oil revenues from a marginal tax change is is −q(t) dτ , whereas the change in
input costs is −c(t)q(t) dτ . As long as c(t) is below its upper bound of 1, the cost effect
therefore dominates, in which case the firm is motivated to move the injection schedule
forward in time. Indeed, panel (a) of Figure 4 does show that the optimal initial injection
rate increases in the tax rate. However, it also shows that the optimal time to switch to
pure water injection is accelerated. As a result, injection rates decline more rapidly over
time the higher is the tax. Even so, the overall effect of higher carbon taxes on cumulative
sequestration is positive, as shown in panel (b). We note in passing that oil production tends
to be insensitive to the level of the carbon tax, which coincides with our earlier observation
that revenue effects from oil sales tend to be more important than input costs in driving the
firms output decisions.
Figure 5 shows CO2 sequestration supply and associated oil output as a function of
the carbon tax. Because the oil extraction paths are very close to their revenue-maximizing
values regardless of the level of the carbon tax, the elasticity of oil output with respect to
the carbon tax is quite small. More surprising is that the sequestration supply curves are
quite inelastic as well. At the current European tax level of about $40/tCO2, the elasticity
of cumulative sequestration is only 0.09, and that of annualized sequestration only 0.10.
5.3. Effects of oil price and carbon tax combined
To recap, the results of subsection 5.1 suggest that the rate of CO2 injection and sequestration
are both relatively responsive to higher oil prices. The result is larger levels of cumulative
sequestration at higher prices. On the other hand, the results of subsection 5.2 indicate
that higher carbon-tax levels increase the optimal CO2 injection rate early on, but reduce it
later, with the same qualitative effects on the induced CO2 sequestration rate. The initial
increase in sequestration dominates, however, resulting in higher overall levels of cumulative
sequestration. Even so, the net impact is relatively small, so that cumulative sequestration
is relatively unresponsive to higher carbon taxes. At tax rates that are high enough to turn
the net CO2 price negative, we also find that oil production is reduced early on, because CO2
20
0 5 10 15 20 25 30 35 40 45
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Time (years)
Rat
e (m
illio
n bl
/yea
r)
tax $0/tCO2tax $40/tCO2tax $80/tCO2tax $120/tCO2
(a)
0 5 10 15 20 25 30 35 40 45
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
Time (years)
Qua
ntity
(m
illio
n bl
)
tax $0/tCO2tax $40/tCO2tax $80/tCO2tax $120/tCO2
(b)
0 5 10 15 20 25 30 35 40 45
0
0.02
0.04
0.06
0.08
0.1
0.12
Time (years)
Rat
e (m
illio
n bl
/yea
r)
waterfloodtax $0/tCO2tax $40/tCO2tax $80/tCO2tax $120/tCO2
(c)
0 5 10 15 20 25 30 35 40 45
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Time (years)
Qua
ntity
(m
illio
n bl
)
waterfloodtax $0/tCO2tax $40/tCO2tax $80/tCO2tax $120/tCO2
(d)
Figure 4. Change in (a) CO2 injection, (b) cumulative sequestration, (c) oilproduction, and (d) cumulative oil production paths as a result of carbon taxchanges.
injection is optimally pushed to levels where its marginal effect on oil production becomes
negative. In effect, the producer sacrifices oil output and revenues early on in return for
higher sequestration revenues that result from higher CO2 injection rates. In this subsection
we combine the two effects of changes in oil price and carbon tax.
21
0 0.2 0.4 0.6 0.8 1 1.2 1.4
0
20
40
60
80
100
120
Cumulative (million bl)
Car
bon
tax
($/tC
O2)
CO2 seq.oil prd.
(a)
0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05
0
20
40
60
80
100
120
Annualized (million bl/year)
Car
bon
tax
($/tC
O2)
CO2 seq.oil prd.
(b)
Figure 5. CO2 sequestration and oil production, both cumulative (a) andannualized (b), as a function of the carbon tax.
Panel (a) of figure 6 shows the combined effect of oil and carbon prices upon the
rate of CO2 injection. The four combinations include oil prices of $100/bl and $200/bl,
with carbon taxes of $40/tCO2 and $80/tCO2. At the time of writing, current oil prices are
about $100/bl while the current carbon the current carbon price in the European market is
roughly $40/tCO2. Thus, one can interpret the variations as corresponding to doubling of
current prices. The important point to take away from this figure is that a doubling of the
carbon tax has a considerably smaller effect on the time path of CO2 injections than does a
doubling of the oil price. Panel (b) of figure 6 shows a similar story for the total amount of
sequestered carbon. While a doubling of the carbon tax does increase the ultimate amount
of sequestered carbon, this effect pales by comparison with the impact due to a doubling of
the oil price.
We conclude the subsection with a discussion of the role played by the incidence of
the carbon tax on the oil price, β. Among the various parameters of the model, this seems
most likely to potentially change the above findings, and is at the same time very difficult
to pin down, While we believe the value β = 1 used in our baseline simulations is defensible,
it seems prudent to investigate the sensitivity of the numerical results with respect to this
22
0 5 10 15 20 25 30 35 40 45
0
0.1
0.2
0.3
0.4
0.5
0.6
Time (years)
Rat
e (m
illio
n bl
/yea
r)
p $100/bl, tax $40/tCO2p $100/bl, tax $80/tCO2p $200/bl, tax $40/tCO2p $200/bl, tax $80/tCO2
(a)
0 5 10 15 20 25 30 35 40 45
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
Time (years)
Qua
ntity
(m
illio
n bl
)
p $100/bl, tax $40/tCO2p $100/bl, tax $80/tCO2p $200/bl, tax $40/tCO2p $200/bl, tax $80/tCO2
(b)
Figure 6. CO2 time paths of injection (a) and cumulative sequestration (b),for various combinations of oil price and carbon tax.
parameter. We therefore replicate the key results from the previous subsection for the two
extreme values of β = 0 and β = 4, corresponding to zero incidence and 100% incidence,
respectively.
6. Conclusion
In this paper, we have examined how the standard resource-economics problem of optimizing
the rate of oil extraction from a field is altered when the producer has the option of increasing
the rate of oil extraction through continuous injections of a mix of CO2 and water into the
reservoir. Such CO2-enhanced oil recovery is a natural stepping stone to future sequestration
of CO2 in saline (non-oil-bearing) aquifers, because incremental oil revenues can pay for
pipelines, injection wells, and other capital infrastructure required.
Our focus in the paper is on the producer’s problem of determining the optimal CO2
injection rate over time. Our theoretical analysis of this problem indicates that, unless oil
prices are increasing at a sufficiently rapid rate, the optimal CO2 injection rate will typically
23
decline over time, and may eventually drop to zero before it becomes optimal to terminate
the extraction process.
Numerical simulations confirm these results and allow us to further investigate com-
parative dynamics of the model. As one would expect, higher oil prices are found to shift
the optimal CO2 injection rate in the direction of output-maximizing levels at each point
in time, but the effect is generally small. This is because the baseline oil price of $100 is
already very high relative to CO2-related costs, and the oil production rate in the baseline
scenario therefore already very close to maximal.
A key finding is that, even though higher carbon taxes do induce higher sequestration,
the effect is quite small: at tax levels comparable to current carbon-credit prices in Europe
(about $40/tCO2), we estimate the elasticity of sequestration supply to be around 0.06.
Our simulation results suggest good news and bad news for potential carbon seques-
tration from EOR. The bad news is that EOR-based carbon sequestration appears to be
highly inelastic. As such, there is little hope that higher carbon prices will induce large
increases in EOR-based sequestration. The good news is that for a range of combinations of
oil price and carbon price, and for what seem to be reasonable parameter values, EOR has
the potential to generate sufficient increases in profits to cover the up-front costs associated
with EOR. The difference between these increases in profits and the up-front costs provides
a legitimate source for funding new infrastructure such as pipelines, which in turn would be
readily available for later use by more efficacious sequestration projects such as the use of
deep saline aquifers. It is also conceivable that the potential gains from undertaking EOR
might stimulate research into better and cheaper techniques for carbon capture. Such im-
provements would be beneficial in their own right, and could plausibly accelerate interest in
sequestration.
Of course, the apparent inelasticity of EOR-based carbon sequestration at the indi-
vidual well level need not imply an inelastic supply at the market level. Because oil reservoirs
are generally not spatially homogeneous with respect to relevant physical parameters such
as depth, temperature, thickness, and injectivity, however, it is conceivable that EOR would
24
be attractive in some sections of a reservoir, but not others, for a given combination of eco-
nomic parameters.13 Moreover, geologic variations across different oil reservoirs will likely
create heterogeneities in the increase in the present value of profits firms can earn relative
to those from a pure water flood. Such differences in the incremental gain from undertaking
EOR can be important considerations as firms contemplate investments that are necessary
to facilitate EOR. There are two main components to these up-front costs. One is the cost
of converting the field to CO2 use, which includes changing well equipment and adding me-
tering equipment and pipelines in the field. The other is the cost of a plant for separating
produced CO2 from the oil, and then dehydrating and recompressing it. While the field
conversion cost is roughly proportional to the number of wells operated, the recycling-plant
cost is roughly proportional to the maximum flow of leaked CO2 that must be processed.14
Accordingly, if one imagines comparing across different reservoirs, it seems likely that EOR
projects would come on-line at different points in time or at different combinations of oil
price and carbon price. This observation suggests that the sequestration supply curve for a
broader geographic entity, such as a state or country as a whole, would likely be more elastic
than is true for the single unit that we study.
One caveat to our results concerns a counter-balancing effect that applies at the larger
geographic level, but is insignificant at the single-unit level. Because EOR will generally raise
oil production, there will be an associated increase in consumption of petroleum-based prod-
ucts, such as motor vehicle fuel. This extra consumption will, of course, generate increased
carbon emissions in its own right. It is not clear how these additional emissions compare to
the sequestration associated with EOR. It is conceivable that, on balance, EOR leads to a
net increase in carbon emissions at the state or national level.
...new paragraph discussing extensions
13 This is true, for example, of the Salt Creek field in Wyoming, one of the largest EOR projects currentlyoperating in the US.14 Based mainly on data in McCoy (2008), and again applying a scaling factor of 1/40 to LSTP’s numberof wells and CO2 throughput, the conversion cost would be $0.6 million and the recycling-plant would cost$2.1 million, for an overall up-front cost of $2.7 million. The practical importance of this number is thatit renders EOR projects unattractive at oil prices below $52 per barrel. In light of current conditions ininternational oil markets, it seems unlikely that we will observe prices in this range going forward.
25
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